Quaternionic quantum mechanics in real Hilbert space

Sergio Giardino

doi:10.1016/j.geomphys.2020.103956

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arXiv · 1803.11523

Quaternionic quantum mechanics in real Hilbert space

Sergio Giardino

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Abstract

A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After a brief discussion on unitary operators in this formalism, we conclude that this quantum theory is indeed consistent, and can be a valuable tool in the search for new physics.

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Sergio Giardino. 2018-03-30. Quaternionic quantum mechanics in real Hilbert space. https://doi.org/10.1016/j.geomphys.2020.103956

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